Robust ℒ2 control for a class of nonlinear systems: A parameter varying Lyapunov function approach

The problem of robustly stabilizing a class of nonlinear systems by using an ℒ₂ state feedback based controller is proposed. A class of nonlinear systems is approximated by a Takagi-Sugeno (T-S) model. A robust stabilization technique is proposed to override the effect of approximation error between the original nonlinear system and the approximated T-S model. A sufficient condition is derived to ensure the robust stability of the ℒ₂ state feedback based controller with guaranteed disturbance attenuation level. Unlike the approaches using a single quadratic Lyapunov function, a parameter varying quadratic Lyapunov function is employed in our approach. A transformation is presented to formulate the problem in terms of a linear matrix inequality problem for which efficient optimization techniques are available. A simulation example of an inverted pendulum on a cart illustrates the performance and the validity of the proposed approach.